Secondary battery system and method for controlling secondary battery

ABSTRACT

An ECU calculates a surface potential of a negative electrode active material relative to a lithium reference potential, according to a battery model for calculating lithium concentration distribution inside the negative electrode active material. The ECU calculates a voltage drop amount associated with charging of a battery, using a charging current to the battery and a reaction resistance, and calculates a negative electrode potential by subtracting the voltage drop amount from the surface potential. The ECU corrects the negative electrode potential, using an SOC of the battery, an average current in a charging period of the battery, and an integrated current in the charging period.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a divisional of U.S. application Ser. No.16/228,984, filed on Dec. 21, 2018, which is a nonprovisionalapplication based on Japanese Patent Application No. 2017-248168, filedon Dec. 25, 2017 with the Japan Patent Office, the entire contents ofwhich are hereby incorporated by reference.

BACKGROUND Field

The present disclosure relates to a secondary battery system and amethod for controlling a secondary battery, and more particularly to atechnique for estimating the state of deposition of lithium on anegative electrode of a lithium ion secondary battery.

Description of the Background Art

In recent years, development of electrically powered vehicles such ashybrid vehicles and electric vehicles has been promoted. Many ofsecondary battery systems mounted in these electrically powered vehiclesadopt a lithium ion secondary battery. This is because, when comparedwith other secondary batteries, a lithium ion secondary batterygenerally has a higher energy density and thus can be downsized, and hasa higher average operation voltage and thus is suitable for generating ahigh voltage. It is known that, in a lithium ion secondary battery,depending on its charged manner, metal lithium (Li) may be deposited ona surface of a negative electrode. This phenomenon will be hereafteralso referred to as “lithium deposition”. Lithium deposition occurs, forexample, when a negative electrode potential falls below a referencepotential (potential of metal lithium) in a case where charging of thelithium ion secondary battery at a high rate (high charging speed),charging thereof in a high SOC (State Of Charge) state, continuouscharging thereof for a long time, and the like are performed. Occurrenceof lithium deposition may cause deterioration in the performance of thelithium ion secondary battery.

Accordingly, there has been proposed a technique of estimating lithiumconcentration distribution inside an active material (in particular, anegative electrode active material), and calculating a negativeelectrode potential based on the estimated result, in order to suppresslithium deposition. For example, with a technique disclosed in JapanesePatent Laying-Open No. 2014-032826, lithium concentration distributionis estimated in consideration of a lithium diffusion phenomenon insidean active material by applying a primitive equation (such as a diffusionequation or an equation representing the principle of conservation ofcharge) to an active material model (see, for example, FIGS. 9 and 10 ofJapanese Patent Laying-Open No. 2014-032826).

SUMMARY

It is also conceivable to calculate a negative electrode potential byconsidering a surface potential of a negative electrode active materialand a voltage drop amount due to a reaction resistance when lithium ionsare inserted from a surface of the negative electrode active materialinto the negative electrode active material (details will be describedlater). However, as a result of studies by the present inventors, it hasbeen found that, when only the two voltage components described aboveare taken into consideration, the accuracy of calculating the negativeelectrode potential may be reduced depending on the charging history ofa lithium ion secondary battery. In such a case, the state of depositionof lithium on a negative electrode of the lithium ion secondary batterymay not be estimated accurately.

The present disclosure has been made to solve the aforementionedproblem, and an object thereof is to accurately estimate the state ofdeposition of lithium on a negative electrode of a lithium ion secondarybattery.

(1) A secondary battery system in accordance with an aspect of thepresent disclosure includes a secondary battery having a negativeelectrode including a negative electrode active material into and fromwhich lithium ions are inserted and desorbed, and a controllerconfigured to calculate a negative electrode potential indicating apotential of the negative electrode relative to a reference potential.The controller is configured to calculate a surface potential of thenegative electrode active material relative to the reference potential,using an amount of lithium ions inserted into the negative electrodeactive material obtained from a charging current to the secondarybattery, and a diffusion coefficient of lithium ions inside the negativeelectrode active material, according to a battery model for calculatinglithium concentration distribution inside the negative electrode activematerial. The controller is configured to calculate a voltage dropamount associated with charging of the secondary battery, using thecharging current to the secondary battery and a reaction resistance ofthe secondary battery, and calculate the negative electrode potential bysubtracting the voltage drop amount from the surface potential. Thecontroller is configured to correct the negative electrode potential,using an SOC of the secondary battery, an average current in a chargingperiod of the secondary battery, and an integrated current in thecharging period.

(2) Preferably, the controller is configured to calculate a depositionovervoltage which promotes deposition of lithium on the negativeelectrode, from the SOC of the secondary battery, the average current,and the integrated current, and correct the negative electrode potentialby further subtracting the deposition overvoltage from the surfacepotential from which the voltage drop amount has been subtracted. Thedeposition overvoltage is a voltage applied from outside of the negativeelectrode active material to a surface of the negative electrode activematerial due to uneven lithium concentration distribution outside thenegative electrode active material.

(3) Preferably, the controller is configured to calculate the depositionovervoltage such that the deposition overvoltage increases (becomeshigher) as the average current increases, and increases (becomes higher)as the integrated current increases.

With the configurations described above in (1) to (3), the negativeelectrode potential is corrected based on the average current and theintegrated current during the charging period of the secondary battery.By this correction, the deposition overvoltage (the voltage applied tothe surface of the negative electrode active material due to unevenlithium concentration distribution outside the negative electrode activematerial, more specifically, uneven lithium concentration distributionin a thickness direction of an electrode assembly) can be reflected inthe negative electrode potential. Therefore, the accuracy of calculatingthe negative electrode potential is improved, and thus the state ofdeposition of lithium on the negative electrode can be estimatedaccurately.

(4) Preferably, the controller is configured to calculate a reactionovervoltage using an equilibrium potential of deposition of lithium onthe negative electrode and dissolution of lithium from the negativeelectrode. When the reaction overvoltage exceeds a predetermined value,the controller is configured to calculate a dissolution overvoltagewhich promotes dissolution of lithium from the negative electrode, fromthe SOC of the secondary battery, the average current, and theintegrated current, and correct the negative electrode potential byadding the dissolution overvoltage to the surface potential from whichthe voltage drop amount has been subtracted.

With the configuration described above in (4), the negative electrodepotential is corrected in consideration of lithium dissolution from thenegative electrode in addition to lithium deposition on the negativeelectrode. By considering both lithium deposition and lithiumdissolution in this manner, the accuracy of calculating the negativeelectrode potential can be further improved. Hence, the state ofdeposition of lithium on the negative electrode can be estimated moreaccurately.

(5) A method for controlling a secondary battery in accordance withanother aspect of the present disclosure is to calculate a negativeelectrode potential of the secondary battery having a negative electrodeincluding a negative electrode active material into and from whichlithium ions are inserted and desorbed. The method for controlling thesecondary battery includes first to fifth steps. The first step is thestep of calculating a surface potential of the negative electrode activematerial, using an amount of lithium ions inserted into the negativeelectrode active material obtained from a charging current to thesecondary battery, and a diffusion coefficient of lithium ions insidethe negative electrode active material, according to a battery model forcalculating lithium concentration distribution inside the negativeelectrode active material. The second step is the step of calculating avoltage drop amount associated with charging of the secondary battery,using the charging current to the secondary battery and a reactionresistance of the secondary battery. The third step is the step ofcalculating the negative electrode potential by subtracting the voltagedrop amount from the surface potential. The fourth step is the step ofcorrecting the negative electrode potential, using an SOC of thesecondary battery, an average current in a charging period of thesecondary battery, and an integrated current in the charging period. Thefifth step is the step of performing protection control for protectingthe negative electrode when the negative electrode potential aftercorrection falls below a reference potential.

With the method described above in (5), the state of deposition oflithium on the negative electrode of the secondary battery can beestimated accurately, as with the configuration described above in (1).

The foregoing and other objects, features, aspects and advantages of thepresent disclosure will become more apparent from the following detaileddescription of the present disclosure when taken in conjunction with theaccompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagram schematically showing an entire configuration of avehicle equipped with a secondary battery system in accordance with afirst embodiment.

FIG. 2 is a diagram showing an example of a configuration of each cell.

FIG. 3 is a diagram showing an example of temporal changes in a positiveelectrode potential and a negative electrode potential during chargingof a battery.

FIG. 4 is a conceptual diagram of a battery model in a comparativeexample.

FIG. 5 is a conceptual diagram of a battery model in the presentembodiment.

FIG. 6 is a diagram for illustrating a negative electrode activematerial model in the present embodiment.

FIG. 7 is a flowchart showing charging current suppression control inthe first embodiment.

FIG. 8 is a diagram for illustrating a technique of calculating anoutermost surface lithium number (process in S104 of FIG. 7) in moredetail.

FIG. 9 is a diagram showing an example of a map for calculating asurface potential.

FIG. 10 is a diagram showing an example of a correction map MP1.

FIG. 11 is a flowchart showing charging current suppression control in asecond embodiment.

FIG. 12 is a diagram showing an example of a correction map MP2.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

Hereinafter, embodiments of the present disclosure will be described indetail with reference to the drawings. It should be noted that identicalor corresponding parts will be designated by the same reference numeralsin the drawings, and the description thereof will not be repeated.

In the following, a description will be given of an exemplaryconfiguration in which a secondary battery system in accordance with thepresent disclosure is mounted in an electrically powered vehicle.Although the electrically powered vehicle is typically a hybrid vehicle(including a plug-in hybrid vehicle), the electrically powered vehicleis not limited thereto. The secondary battery system in accordance withthe present disclosure is applicable to any vehicle which generatesmotive power using electric power supplied from a secondary batterysystem. Accordingly, the electrically powered vehicle may be an electricvehicle or a fuel cell vehicle. In addition, the secondary batterysystem in accordance with the present disclosure is not limited to beapplied to vehicles, and may be applied to stationary machinery, forexample.

[First Embodiment]

<Configuration of Secondary Battery System>

FIG. 1 is a diagram schematically showing an entire configuration of avehicle equipped with a secondary battery system in accordance with afirst embodiment. Referring to FIG. 1, a vehicle 1 is a hybrid vehicle.Vehicle 1 includes a secondary battery system 2, a power control unit(PCU) 30, motor generators 41 and 42, an engine 50, a power split device60, a drive shaft 70, and a drive wheel 80. Secondary battery system 2includes a battery 10, a monitoring unit 20, and an electronic controlunit (ECU) 100.

Engine 50 is an internal combustion engine which outputs motive power byconverting combustion energy generated by combusting an air-fuel mixturecontaining air and fuel, into kinetic energy of moving elements such asa piston and a rotor.

Power split device 60 includes a planetary gear mechanism (not shown)having three rotation shafts of a sun gear, a carrier, and a ring gear,for example. Power split device 60 splits the motive power output fromengine 50 into motive power for driving motor generator 41 and motivepower for driving drive wheel 80.

Each of motor generators 41 and 42 is an alternating current (AC)rotating electrical machine, and for example is a three-phase ACsynchronous motor with a permanent magnet (not shown) embedded in arotor. Motor generator 41 is used mainly as a power generator driven byengine 50 via power split device 60. Electric power generated by motorgenerator 41 is supplied to motor generator 42 or battery 10 via PCU 30.

Motor generator 42 operates mainly as a motor, and drives drive wheel80. Motor generator 42 is driven by receiving at least one of electricpower from battery 10 and the electric power generated by motorgenerator 41, and a drive force of motor generator 42 is transmitted todrive shaft 70. On the other hand, during braking of the vehicle orwhile acceleration is reduced at a descending slope, motor generator 42operates as a power generator and performs regenerative powergeneration. Electric power generated by motor generator 42 is suppliedto battery 10 via PCU 30.

Battery 10 is configured to include a plurality of cells 10A. Battery 10stores electric power for driving motor generators 41 and 42, andsupplies the electric power to motor generators 41 and 42 through PCU30. In addition, when motor generators 41 and 42 generate electricpower, battery 10 receives the generated electric power through PCU 30and is charged.

Monitoring unit 20 includes a voltage sensor 21, a current sensor 22,and a temperature sensor 23. Voltage sensor 21 detects a voltage VB foreach block (module) including a plurality of cells 10A connected inparallel with each other, for example. Current sensor 22 detects acurrent IB input/output to/from battery 10. Temperature sensor 23detects a temperature TB for each block. Each sensor outputs a signalindicating its detection result to ECU 100.

It should be noted that the unit of monitoring by voltage sensor 21 andtemperature sensor 23 is not limited to a block, and may be a cell 10A,or may be a plurality of adjacent cells 10A (in a number less than thenumber of cells within the block). Since the internal configuration ofbattery 10 does not have an influence in particular in the presentembodiment, there is no need to distinguish the plurality of cells 10Afrom each other or distinguish a plurality of blocks from each other.Accordingly, in the following, battery 10 will be considered as the unitof monitoring, and a comprehensive description such as “voltage VB ofbattery 10 is detected” will be used.

PCU 30 performs bidirectional power conversion between battery 10 andmotor generators 41, 42 according to a control signal from ECU 100. PCU30 is configured to separately control the states of motor generators 41and 42. For example, PCU 30 can set motor generator 42 to a powerrunning state while setting motor generator 41 to a regenerative state(power generation state). PCU 30 is configured to include, for example,two inverters (not shown) provided corresponding to motor generators 41and 42, and a converter (not shown) which boosts a direct current (DC)voltage to be supplied to each inverter to be more than or equal to anoutput voltage of battery 10.

ECU 100 is configured to include a CPU (Central Processing Unit) 101, amemory (ROM (Read Only Memory) and RAM (Random Access Memory)) 102, andinput/output ports (not shown) for inputting/outputting various signals.ECU 100 controls charging and discharging of battery 10 by controllingengine 50 and PCU 30 based on the signal received from each sensor andprograms and maps stored in memory 102. Main processing and controlperformed by ECU 100 include “negative electrode potential calculationprocessing” for calculating a negative electrode potential V2 of battery10 and “charging current suppression control” for suppressing a chargingcurrent to battery 10, for the purpose of protecting battery 10. Thenegative electrode potential calculation processing and the chargingcurrent suppression control will be described later in detail.

FIG. 2 is a diagram showing an example of a configuration of each cell10A. Referring to FIG. 2, each cell 10A is a lithium ion secondarybattery. An upper surface of a case of cell 10A is sealed with a coverbody 11. Cover body 11 is provided with a positive electrode terminal 12and a negative electrode terminal 13. One ends of positive electrodeterminal 12 and negative electrode terminal 13 protrude outward fromcover body 11. The other ends of positive electrode terminal 12 andnegative electrode terminal 13 are electrically connected to an internalpositive electrode terminal and an internal negative electrode terminal(both not shown), respectively, inside a case 111.

An electrode assembly 14 is accommodated inside case 111 (in FIG. 2,electrode assembly 14 is seen through case 111 and is indicated bybroken lines). Electrode assembly 14 is formed, for example, by windinga positive electrode (positive electrode sheet) 15 and a negativeelectrode (negative electrode sheet) 16 stacked with a separator 17interposed therebetween, into a tubular shape. Positive electrode 15includes a current collecting foil 151 (see FIG. 4), and a positiveelectrode active material layer (a layer including a positive electrodeactive material, a conductive material, and a binder) formed on asurface of current collecting foil 151. Similarly, negative electrode 16includes a current collecting foil 161, and a negative electrode activematerial layer (a layer including a negative electrode active material,a conductive material, and a binder) formed on a surface of currentcollecting foil 161. Separator 17 is provided to contact both thepositive electrode active material layer and the negative electrodeactive material layer. Electrode assembly 14 (the positive electrodeactive material layer, the negative electrode active material layer, andseparator 17) is impregnated with an electrolytic solution.

As materials for positive electrode 15, negative electrode 16, separator17, and the electrolytic solution, a variety of conventionally knownmaterials can be used. As an example, lithium cobalt oxide or lithiummanganese oxide is used for positive electrode 15. Aluminum is used forcurrent collecting foil 151 of positive electrode 15. Carbon (graphite)is used for negative electrode 16. Copper is used for current collectingfoil 161 of negative electrode 16. Polyolefin is used for separator 17.The electrolytic solution includes an organic solvent, lithium ions, andan additive.

It should be noted that electrode assembly 14 does not have to be formedas a wound body, and electrode assembly 14 may be a stacked body whichis not wound. In addition, although the present embodiment describes anexample where cell 10A is an ordinary lithium ion secondary battery (aso-called liquid-based battery), the “lithium ion secondary battery” inthe present disclosure may include a lithium polymer battery which usesa polymer gel as an electrolyte.

<Deposition of Metal Lithium on Surface of Negative Electrode>

In secondary battery system 2 configured as described above, voltage VBincreases as battery 10 is charged. On this occasion, changes in apositive electrode potential V1 and negative electrode potential V2occur.

FIG. 3 is a diagram showing an example of temporal changes in positiveelectrode potential V1 and negative electrode potential V2 duringcharging of battery 10. In FIG. 3, the axis of abscissas represents anelapsed time from the start of charging of battery 10, and the axis ofordinates represents a potential relative to a potential of metallithium which is a reactive material within negative electrode 16(lithium reference potential).

Referring to FIG. 3, positive electrode potential V1 is the potential ofpositive electrode 15 relative to the lithium reference potential.Negative electrode potential V2 is the potential of negative electrode16 relative to the lithium reference potential. Voltage VB of battery 10is a potential difference (V1−V2) between positive electrode potentialV1 and negative electrode potential V2. By continuously charging battery10, positive electrode potential V1 increases, whereas negativeelectrode potential V2 decreases, and thereby voltage VB increases.

Generally, when the potential of a negative electrode active materialfalls below the potential of a reactive material, deposition of thereactive material occurs. That is, in battery 10, when negativeelectrode potential V2 becomes less than or equal to the lithiumreference potential (=0 V), metal lithium is deposited on a surface ofthe negative electrode. Therefore, during charging of battery 10,decrease of negative electrode potential V2 is prevented by suppressinga charging current, for example, to maintain negative electrodepotential V2 to be higher than the lithium reference potential (thecharging current suppression control described later). This preventslithium deposition on the surface of the negative electrode.

Conversely, when the potential of the negative electrode active materialexceeds the potential of a reactive material, dissolution of thereactive material occurs. That is, when negative electrode potential V2is higher than the lithium reference potential, metal lithium depositedon the surface of the negative electrode is dissolved in theelectrolytic solution. Such dissolution of metal lithium will bedescribed in a second embodiment.

<One-Dimensional Battery Model>

In order to calculate negative electrode potential V2, it is required toestablish a battery model which simplifies battery 10. For easierunderstanding of the battery model adopted in the present embodiment, abattery model in a comparative example will be briefly described firstin the following. It should be noted that lithium ions and metal lithiumare also comprehensively described as “lithium”.

FIG. 4 is a conceptual diagram of a battery model in a comparativeexample. Referring to FIG. 4, in the battery model in the comparativeexample, positive electrode 15 is composed of an aggregate of a numberof positive electrode active materials 18. Similarly, negative electrode16 is composed of an aggregate of a number of negative electrode activematerials 19. However, FIG. 4 shows one positive electrode activematerial 18 and one negative electrode active material 19 due to spacelimitation.

A coordinate x extending in a lateral direction in FIG. 4 indicates aposition in a thickness direction of electrode assembly 14, that is, adirection in which positive electrode 15 and negative electrode 16 arestacked with separator 17 interposed therebetween. In this manner, thecomparative example adopts a one-dimensional model which includesposition x in the thickness direction of electrode assembly 14 as aparameter but does not consider a position in an in-plane direction ofelectrode assembly 14 in particular. Negative electrode potential V2 canbe calculated by simultaneously solving various primitive equations inthe one-dimensional model. It should be noted that, since theseprimitive equations are described for example in Japanese PatentLaying-Open No. 2014-032826 as equations (1) to (14), the detaileddescription thereof will not be repeated.

<Zero-Dimensional Battery Model>

ECU 100 serving as a vehicle-mounted ECU has a limited computingresource (computing capacity), when compared with a typical computer forresearch and development (for example, a computer for simulation).Therefore, the present embodiment adopts a more simplifiedzero-dimensional battery model in order to reduce a computing load ofECU 100 and shorten a computing time of ECU 100.

FIG. 5 is a conceptual diagram of a battery model in the presentembodiment. Referring to FIG. 5, the present embodiment adopts azero-dimensional battery model which assumes that only one particle ofpositive electrode active material 18 and only one particle of negativeelectrode active material 19 exist, as shown in FIG. 5. Morespecifically, although positive electrode 15 includes a number ofpositive electrode active materials 18, a number of positive electrodeactive materials 18 are represented by single positive electrode activematerial 18, based on an assumption that an electrochemical reaction ineach positive electrode active material 18 is uniform. Similarly, anumber of negative electrode active materials 19 included in negativeelectrode 16 are represented by single negative electrode activematerial 19.

After adopting the battery model simplified as described above, negativeelectrode potential V2 is calculated. A negative electrode activematerial model will now be described in more detail.

FIG. 6 is a diagram for illustrating a negative electrode activematerial model in the present embodiment. Referring to FIG. 6, negativeelectrode active material 19 is virtually divided into N layers in aradial direction r. In the following, an example where N=5 will bedescribed. However, N is not particularly limited as long as N is two ormore. The divided five layers will be described as L₁ to L₅ from acenter O toward an outer circumference of negative electrode activematerial 19. The distance in radial direction r of negative electrodeactive material 19 is 0 at center O of negative electrode activematerial 19, and Dout at an outer surface (outermost surface) ofnegative electrode active material 19. It should be noted thatthicknesses of layers L_(n) (n=1 to 5) may be different from each otheras shown in FIG. 6, or may be equal.

In the present embodiment, negative electrode potential V2 in a region A(a diagonally shaded region) in the outer surface of negative electrodeactive material 19 in which lithium deposition occurs is calculated. Tocalculate negative electrode potential V2 in lithium deposition regionA, it is conceivable to consider two voltage components described below.

A first voltage component is a “surface potential U2” which indicates apotential determined according to lithium concentrations within layersL₁ to L₅ (lithium concentration distribution). Although details will bedescribed later, surface potential U2 is calculated in consideration ofdiffusion of lithium inside negative electrode active material 19. Asecond voltage component is a “voltage drop amount ΔV due to a reactionresistance” when lithium is input/output to/from the outer surface ofnegative electrode active material 19 (lithium is input duringcharging). It should be noted that the reaction resistance means animpedance component associated with transmission and reception of charge(charge transfer) at an interface between the electrolytic solution andthe outer surface of negative electrode active material 19.

As a result of studies by the present inventors, it has been found that,in the negative electrode potential calculation processing which adoptsthe zero-dimensional battery model as in the present embodiment, whenonly the two voltage components described above are taken intoconsideration, the accuracy of calculating negative electrode potentialV2 may be reduced depending on the charging history of battery 10. Morespecifically, when battery 10 is charged with a relatively largecurrent, reduction in the accuracy of calculating negative electrodepotential V2 tends to be significant.

This is considered to be because, unlike the one-dimensional batterymodel (see FIG. 4) as in the comparative example, the zero-dimensionalbattery model does not consider the lithium concentration distributionin thickness direction x of electrode assembly 14 (that is, the lithiumconcentration distribution outside positive electrode active material 18and negative electrode active material 19, such as in the electrolyticsolution). Although uneven lithium distribution associated with chargingof battery 10 may also occur outside the active materials, when battery10 is charged with a large current, the speed at which lithiumdistribution becomes uneven (the speed at which unevenness of thelithium concentration distribution increases) is relatively faster thanthe speed at which lithium is diffused (the speed at which unevenness isrelieved). Accordingly, diffusion of lithium fails to keep up with thespeed at which lithium distribution becomes uneven, and as a result, avoltage due to uneven lithium concentration distribution is applied tothe outer surface of negative electrode active material 19. Since thisvoltage component promotes lithium deposition on the surface of thenegative electrode (lithium deposition region A), this voltage componentis also described as a “deposition overvoltage ηp”.

Therefore, in the present embodiment, negative electrode potential V2 iscalculated considering deposition overvoltage ηp according to thecharging history of battery 10. More specifically, negative electrodepotential V2 calculated from the two voltage components described aboveis corrected using an average current IBave and an integrated currentΘIB of battery 10 during charging of battery 10. Through thiscorrection, the accuracy of calculating negative electrode potential V2can be improved while shortening the computing time, which is anadvantage of the zero-dimensional model, as described below.

<Flow of Charging Current Suppression Control>

FIG. 7 is a flowchart showing the charging current suppression controlin the first embodiment. The flowcharts shown in FIG. 7 and FIG. 10described later are performed each time a predetermined computing cycle(for example, approximately 100 milliseconds) elapses during charging ofbattery 10, for example. Although each step (hereinafter abbreviated asS) in these flowcharts is basically implemented by software processingperformed by ECU 100, each step may be implemented by hardwareprocessing performed by electric circuitry fabricated within ECU 100.

In the following, a period starting from the start of charging ofbattery 10 will be referred to as a “charging period”. In a case wherecharging of battery 10 for which charging/discharging has been stoppedis started, the charging period means a period starting from the end ofthe stop (=the start of charging). Further, in a case where thedirection of charging/discharging battery 10 is switched as vehicle 1travels, for example, the charging period means a period starting fromthe switching from discharging to charging. It is assumed that ECU 100calculates average current IBave indicating an average value of currentIB during the charging period, and integrated current ΘIB indicating anintegrated value of current IB during the charging period, in otherflows now shown.

Referring to FIG. 7, in S101, ECU 100 acquires the detection result ofeach sensor within monitoring unit 20. Specifically, ECU 100 acquiresvoltage VB of battery 10 detected by voltage sensor 21. ECU 100 acquirescurrent IB input/output to/from battery 10 detected by current sensor22. ECU 100 acquires temperature TB of battery 10 detected bytemperature sensor 23.

In S102, ECU 100 calculates a lithium number input to negative electrodeactive material 19 (more specifically, outermost layer L₅ of negativeelectrode active material 19), from current IB acquired in S101.Specifically, a current density (unit:

C/(m²·s)) is calculated by dividing current IB (unit: A=C/s) by the areaof plates of positive electrode 15 and negative electrode 16 inelectrode assembly 14. By multiplying the current density by thecomputing cycle (unit: s) and an inflow coefficient (unit: m²), a chargeamount (unit: C) input/output to/from negative electrode active material19 is obtained. Since the charge amount of each lithium ion is known,the lithium number input/output to/from negative electrode activematerial 19 can be obtained by dividing the charge amount input/outputto/from negative electrode active material 19 by the charge amount ofeach lithium ion.

In S103, ECU 100 calculates lithium numbers Ni to Ns included in layersL₁ to L₅, respectively, in consideration of lithium diffusion betweenadjacent layers of layers L_(n) (n=1 to 5). Specifically, a calculationtechnique as described below can be used. Namely, a lithium numberwithin layer L_(n) in an m-th computing cycle (m is a natural number) isdescribed as N_(n)(m). In that case, lithium number N_(n)(m) withinlayer L_(n) is represented by the following equation (1):

$\begin{matrix}{{N_{n}\left( {m + 1} \right)} = {{N_{n}(m)} + {{N_{n}}^{in}(m)} - {{N_{n}}^{out}(m)}}} & (1)\end{matrix}$

In equation (1), a lithium inflow number from another adjacent layer tolayer L_(n) is described as N_(n) ^(in)(m), and a lithium outflow numberfrom layer L_(n) to an adjacent layer is described as N_(n) ^(out)(m).Lithium inflow number N_(n) ^(in)(m) to layer L_(n) is represented bythe following equation (2):

$\begin{matrix}{{{N_{n}}^{in}(m)} = {{D \times C_{n + 1} \times \Delta{N_{n + 1}(m)}} + {D \times A_{n} \times \Delta{N_{n}(m)}}}} & (2)\end{matrix}$

On the other hand, lithium outflow number N_(n) ^(out)(m) from layerL_(n) is represented by the following equation (3):

$\begin{matrix}{{{N_{n}}^{out}(m)} = {{D \times A_{n + 1} \times \Delta{N_{n + 1}(m)}} + {D \times C_{n} \times \Delta{N_{n}(m)}}}} & (3)\end{matrix}$

In the above equations (2) and (3), D is a diffusion coefficient. C andA are constants for correcting different surface areas (areas ofspherical layer surfaces shown in FIG. 6) between adjacent layers. Morespecifically, constant C is a correction constant in consideration of adifference in surface area in lithium inflow from an outer layer (layerL_(n+1)) to an inner layer (layer L_(n)) adjacent to the outer layer.Conversely, constant A is a correction constant in consideration of adifference in surface area in lithium outflow from an inner layer to anouter layer adjacent to the inner layer. ΔN_(n+1) is a difference inlithium number between layer L_(n+1) and layer L_(n). ΔN_(n) is adifference in lithium number between layer L_(n) and layer L_(n−1).Lithium number N_(n)(m) within layer L_(n) can be calculated by givingan initial value (N_(n)(0)) for all layers L_(n) (n=1 to 5) andrepeatedly solving the above equations (1) to (3).

In S104, ECU 100 calculates a lithium number existing in the outermostsurface of negative electrode active material 19, from lithium numbersN₄ and N₅ calculated in S103. This lithium number will be described asan “outermost surface lithium number Nout”. Outermost surface lithiumnumber Nout is calculated as described below.

FIG. 8 is a diagram for illustrating a technique of calculatingoutermost surface lithium number Nout (process in S104 of FIG. 7) inmore detail. In FIG. 8, the axis of abscissas represents a distancealong radial direction r of negative electrode active material 19. Theposition of center O of negative electrode active material 19 isindicated by a distance O, and the distance increases toward the outsideof negative electrode active material 19. The axis of ordinatesrepresents the calculated result of the lithium number at each position.

Referring to FIG. 8, lithium numbers N₁ to N₅ are already calculated bythe process in S103. Here, it is assumed that lithium number N₄ withinlayer L₄ indicates a lithium number at an exactly intermediate distancebetween an innermost distance and an outermost distance of layer L₄ (seeFIG. 6). It is also assumed that lithium number Ns within layer Lsindicates a lithium number at an exactly intermediate distance betweenan innermost distance and an outermost distance (=a distancecorresponding to the outermost surface of negative electrode activematerial 19) of layer L₅. Thus, a straight line J which connects a point(D₄, N₄) indicating lithium number N₄ within layer L₄ and a point (D₅,N₅) indicating lithium number N₅ within layer L₅ can be obtained. Byextrapolating straight line J to a position at the outermost surface(having distance Dout), a point (Dout, Nout) is obtained.

Turning back to FIG. 7, in S105, ECU 100 calculates surface potential U2from outermost surface lithium number Nout. Generally, the surfacepotential of an active material is determined according to the amount ofthe active material existing in a surface of the active material.Therefore, the correlation between outermost surface lithium number Noutand surface potential U2 is obtained by a preliminary experiment, and isstored as a map MP0 in memory 102 of ECU 100, for example.

FIG. 9 is a diagram showing an example of map MP0 for calculatingsurface potential U2. In FIG. 9, the axis of abscissas representsoutermost surface lithium number Nout, and the axis of ordinatesrepresents surface potential U2. As shown in FIG. 9, surface potentialU2 decreases as outermost surface lithium number Nout increases. Byreferring to this map MP0, ECU 100 can calculate surface potential U2from outermost surface lithium number Nout. It should be noted that afunction or a conversion equation may be prepared instead of a map.

Referring to FIG. 7 again, in S106, ECU 100 calculates voltage dropamount AV due to the reaction resistance (ΔV>0). Voltage drop amount AVcan be calculated according to the Butler-Volmer equation represented bythe following equation (4):

$\begin{matrix}{V = {\frac{RT_{B}}{\alpha\beta F}{\sinh^{- 1}\left( \frac{{- \beta}\; I}{2{Lai}_{0}{k/g}} \right)}}} & (4)\end{matrix}$

It should be noted that, in equation (4), R indicates the reactionresistance, F indicates the Faraday constant, α indicates a chargetransfer coefficient, a indicates a specific surface area of negativeelectrode active material 19, L indicates a film thickness of negativeelectrode active material 19, i₀ indicates an exchange current density,k indicates a standard speed constant, and g indicates activationenergy. I is the product of a current density and a deposition surfacearea. When negative electrode potential V2 (=U2−ΔV) is 0, the relationU2=ΔV (=IR) is satisfied.

Therefore, voltage drop amount ΔV can be calculated by substituting U2for V into equation (4) and solving equation (4) for IR.

In S107, ECU 100 calculates negative electrode potential V2 bysubtracting voltage drop amount AV calculated in S106 from surfacepotential U2 calculated in S105 (V2=U2−ΔV). It should be noted that theprocesses in S101 to S107 correspond to the negative electrode potentialcalculation processing.

In S108, ECU 100 estimates the SOC of battery 10 based on the detectionresult of each sensor within monitoring unit 20 acquired in S101. As atechnique for estimating the SOC, a variety of known techniques such asthe current integration method can be used.

In S109, ECU 100 acquires average current IBave in the charging periodand integrated current ΣIB in the charging period. As described above,average current IBave and integrated current ΣIB are calculated in otherflows now shown, based on a detection value (current IB) of currentsensor 22.

Memory 102 of ECU 100 stores a correction map MP1 described later. Byreferring to correction map MP1, ECU 100 calculates depositionovervoltage ηp for correcting negative electrode potential V2, from theSOC of battery 10 estimated in S108 and average current IBave andintegrated current ΣIB acquired in S109 (S110).

FIG. 10 is a diagram showing an example of correction map MP1. Referringto FIG. 10, in correction map MP1, deposition overvoltage ηp is definedfor each combination of the SOC of battery 10, average current IBave,and integrated current ΣIB (SOC, IBave, ΣIB) based on the result of apreliminary experiment. As indicated by an arrow in the drawing,deposition overvoltage ηp becomes higher from the lower left to theupper right in the drawing. That is, deposition overvoltage ηp becomeshigher as average current IBave increases, and becomes higher asintegrated current ΣIB increases. It is described for confirmation thatthe concrete numerical values shown in FIG. 10 are merely examples forfacilitating understanding.

The reason why two parameters, average current IBave and integratedcurrent ΣIB, are used as current-related parameters will be described.For example, comparison is made between a first charging pattern inwhich current IB is constant at 10 A during a charging period of 10seconds and a second charging pattern in which current IB is alsoconstant at 10 A during a charging period of 20 seconds. In the firstcharging pattern and the second charging pattern, average current IBaveis equal, whereas integrated current ΣIB is different. In this case, thelithium concentration distribution in thickness direction x of electrodeassembly 14 tends to become more uneven in the second charging patternin which integrated current ΣIB is relatively large, when compared withthe first charging pattern. By using integrated current ΣIB as aparameter, such a difference can be reflected in deposition overvoltageηp.

In addition, for example, comparison is made between the above firstcharging pattern in which current IB is constant at 10 A during acharging period of 10 seconds and a third charging pattern in whichcurrent IB is constant at 20 A during a charging period of 5 seconds. Inthe first charging pattern and the third charging pattern, integratedcurrent ΣIB is equal, whereas average current IBave is different. Inthis case, the lithium concentration distribution in thickness directionx of electrode assembly 14 tends to become more uneven in the thirdcharging pattern in which average current IBave is relatively large,when compared with the first charging pattern. By using average currentIBave as a parameter, such a difference can also be reflected indeposition overvoltage

It should be noted that, although FIG. 10 shows an example of athree-dimensional map including three parameters (SOC, IBave, ΣIB), afour-dimensional map further including temperature TB of battery 10 maybe prepared. Thereby, deposition overvoltage ηp can be calculated withhigher accuracy.

Referring to FIG. 7 again, in S111, ECU 100 corrects negative electrodepotential V2, using deposition overvoltage ηp obtained by referring tocorrection map MP1. Negative electrode potential V2 after correction isa potential obtained by subtracting deposition overvoltage ηp fromnegative electrode potential V2 before correction (=U2−ΔV) (V2−ηp→V2).

In S112, ECU 100 determines whether or not lithium deposition onnegative electrode 16 may occur, based on negative electrode potentialV2 after correction.

Specifically, ECU 100 determines whether or not negative electrodepotential V2 after correction is less than or equal to the lithiumreference potential, that is, whether or not negative electrodepotential V2 is less than or equal to 0 V (V2≤0).

When negative electrode potential V2 after correction is less than orequal to 0 V (YES in S112), ECU 100 assumes that lithium deposition onnegative electrode 16 may occur and advances the processing to S113, andperforms the charging current suppression control. Since this chargingcurrent suppression control is equal to the control described in FIG. 5of Japanese Patent Laying-Open No. 2012-244888, for example, detaileddescription thereof will not be repeated. However, for example, an inputcurrent limit target value Itag is calculated based on a current IB(t)and an acceptable input current Ilim(t) at a time t, by offsetting apredetermined amount relative to Ilim(t). Then, based on obtained Itag,Win(t) indicating a control upper limit value of charging power tobattery 10 is calculated. Thereafter, the processing is returned to amain routine not shown.

It should be noted that, when negative electrode potential V2 aftercorrection is higher than 0 V (NO in S112), ECU 100 assumes that lithiumdeposition on negative electrode 16 may not occur and skips the processin S113, and returns the processing to the main routine.

As described above, according to the first embodiment, negativeelectrode potential V2 is corrected based on average current IBave andintegrated current DB during the charging period of battery 10. By thiscorrection, deposition overvoltage ηp (that is, the voltage applied tothe outer surface of negative electrode active material 19 due to unevenlithium concentration distribution in thickness direction x of electrodeassembly 14) can be reflected in negative electrode potential V2.Therefore, the accuracy of calculating negative electrode potential V2is improved, and thus the state of deposition of lithium on negativeelectrode 16 can be estimated accurately.

Further, the parameters (the SOC, average current IBave, and integratedcurrent ΣIB) in correction map MP1 used to calculate depositionovervoltage ηp can each be calculated by simple computation. Hence,according to the present embodiment, the accuracy of estimating thestate of deposition of lithium on negative electrode 16 can be improvedwhile maintaining reduction of the computing load and shortening of thecomputing time, which are advantages of the zero-dimensional model.

[Second Embodiment]

The first embodiment describes that negative electrode potential V2 iscorrected using deposition overvoltage ηp calculated from correction mapMP1. On the other hand, lithium once deposited on lithium depositionregion A of negative electrode active material 19 (see FIG. 6) is notnecessarily maintained in that state, and may be dissolved in theelectrolytic solution and return to lithium ions. The second embodimentwill describe a configuration which considers lithium dissolution inaddition to lithium deposition.

FIG. 11 is a flowchart showing charging current suppression control inthe second embodiment. Referring to FIG. 11, since the negativeelectrode potential calculation processing in S200 is equal to thenegative electrode potential calculation processing in the firstembodiment (processes in S101 to S107 of FIG. 7), the descriptionthereof will not be repeated. In addition, since the process in S201 andthe process in S202 are also equal to the process in S108 and theprocess in S109 in the first embodiment, respectively, the descriptionthereof will not be repeated.

In S203, ECU 100 determines whether or not negative electrode potentialV2 before correction is less than or equal to 0 V (V2≤0). When negativeelectrode potential V2 before correction is less than or equal to 0 V(YES in S203), ECU 100 assumes that lithium deposition may occur andadvances the processing to S205, and calculates a reaction overvoltage ϕof lithium deposition/dissolution reactions.

Reaction overvoltage ϕ can be calculated from surface potential U2, anequilibrium potential Ueq of the deposition reaction and the dissolutionreaction, and voltage drop amount ΔV due to the reaction resistance, asrepresented by the following equation (5). It should be noted that,since equilibrium potential Ueq is a known value, reaction overvoltage ϕcan be calculated from negative electrode potential V2 before correction(=U2−ΔV).

$\begin{matrix}{\phi = {{U2} - {Ueq} - {\Delta V}}} & (5)\end{matrix}$

In S206, ECU 100 determines whether reaction overvoltage ϕ is positiveor negative. When reaction overvoltage ϕ is negative (ϕ<0 in S206), ECU100 determines that lithium deposition on lithium deposition region Aoccurs, and advances the processing to S207. The process in S207 and theprocess in S208 are equal to the process in S110 and the process in S111in the first embodiment, respectively.

On the other hand, when reaction overvoltage ϕ is 0 or positive (ϕ≥0 inS206), ECU 100 determines that lithium dissolution from lithiumdeposition region A occurs, and advances the processing to S209. Then,ECU 100 calculates a dissolution overvoltage ηd from the SOC of battery10, average current IBave, and integrated current ΣIB, by referring to acorrection map MP2. FIG. 12 is a diagram showing an example ofcorrection map MP2. Also in correction map MP2 shown in FIG. 12, as incorrection map MP1, dissolution overvoltage μd is defined for eachcombination of the SOC of battery 10, average current IBave, andintegrated current ΣIB (SOC, IBave, ΣIB). As indicated by an arrow inthe drawing, dissolution overvoltage ηd also becomes higher from thelower left to the upper right in the drawing.

Returning back to FIG. 11, in S210, ECU 100 corrects negative electrodepotential V2, using dissolution overvoltage ηd obtained by referring tocorrection map MP2. More specifically, dissolution overvoltage ηd isadded to negative electrode potential V2 before correction (V2+ηd→V2).

In this manner, when lithium deposition occurs, correction of negativeelectrode potential V2 is performed by the process in S208, whereas whenlithium dissolution occurs, correction of negative electrode potentialV2 is performed by the process in S210. Then, it is determined whetheror not negative electrode potential V2 after correction is less than orequal to 0 V (S211). The processes in and after S211 are equal to thecorresponding processes in the first embodiment.

It should be noted that, when negative electrode potential V2 beforecorrection is higher than 0 V (NO in S203), it is determined whether ornot there is a history of lithium deposition (S204). When there is ahistory of lithium deposition (YES in S204), it is assumed thatdissolution of deposited lithium may occur, and the processing isadvanced to S209. On the other hand, when there is no history of lithiumdeposition (NO in S204), no lithium dissolution occurs either, and thussubsequent processes are all skipped and the processing is returned tothe main routine.

As described above, according to the second embodiment, negativeelectrode potential V2 is corrected in consideration of lithiumdissolution from lithium deposition region A in addition to lithiumdeposition on lithium deposition region A. By considering both lithiumdeposition and lithium dissolution in this manner, the accuracy ofcalculating negative electrode potential V2 can be further improved.Hence, the state of deposition of lithium on negative electrode 16 canbe estimated more accurately.

Although the embodiments of the present disclosure have been described,it should be understood that the embodiments disclosed herein areillustrative and non-restrictive in every respect. The scope of thepresent disclosure is defined by the scope of the claims, and isintended to include any modifications within the scope and meaningequivalent to the scope of the claims.

What is claimed is:
 1. A method for controlling a secondary battery, forcalculating a negative electrode potential of the secondary batteryhaving a negative electrode including a negative electrode activematerial into and from which lithium ions are inserted and desorbed, themethod comprising: calculating a surface potential of the negativeelectrode active material, using an amount of lithium ions inserted intothe negative electrode active material obtained from a charging currentto the secondary battery, and a diffusion coefficient of lithium ionsinside the negative electrode active material, according to a batterymodel for calculating lithium concentration distribution inside thenegative electrode active material; calculating a voltage drop amountassociated with charging of the secondary battery, using the chargingcurrent to the secondary battery and a reaction resistance of thesecondary battery; calculating the negative electrode potential bysubtracting the voltage drop amount from the surface potential;correcting the negative electrode potential, using an SOC of thesecondary battery, an average current in a charging period of thesecondary battery, and an integrated current in the charging period; andperforming protection control for protecting the negative electrode whenthe negative electrode potential after correction falls below areference potential.